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We provide an analytical solution of the heat equation in the half-spacesubject to a moving Gaussian heat flux with piecewise constant parameters. Thesolution is of interest in powder bed fusion applications where theseparameters can be used to control the conduction of heat due to a scanning beamof concentrated energy. The analytical solution is written in a dimensionlessform as a sum of integrals over (dimensionless) time. For the numericalcomputation of these integrals we suggest a quadrature scheme that utilizespre-calculated look-up tables for the required quadrature orders. Such a schemeis efficient because the required quadrature orders are strongly dependent onthe parameters in the heat flux. The possibilities of using the obtainedcomputational technique for the control and optimization of powder bed fusionprocesses are discussed.

Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters